Broadband beamforming is a widely used technique for directionally receiving signals such as acoustic or radio waves. Beamforming techniques have been described in the context of e.g. sound source localisation, sonar, radar, wireless communication etc. Generally, in such systems, the signals from the sensors are amplified and delayed in such a manner that the resulting measurement system is particularly sensitive to waves coming from a certain direction. In such a measurement system it is possible to steer the sensitivity of an array of sensors to a certain direction—a process known as ‘beamforming’. When all channels are recorded simultaneously such a system requires only a very small amount of time for a single measurement.
For example, many noise abatement problems involve localizing one or several sources of noise in a complex environment such as the interior of a car or an aircraft. In recent years it has become possible to perform measurements using many channels simultaneously. Today, measurement systems exists with a large number of microphones (e.g. 64 or 128) mounted in a grid. In other measurement systems the microphones are typically mounted in a less regular configuration.
Due to the cost of microphones (or other sensors) and data/signal acquisition hardware, it is generally desirable to use as few sensors as possible in a beamforming system. On the other hand requirements to the frequency range and to the spatial precision of the system both tend to increase the number of sensors needed in the array.
In the so-called Filter-And-Sum (FAS) beamforming, an output time signal at a given position is computed by applying individual filters to the sensor signals followed by an addition of the filtered signals. The article “Convex optimization based time-domain broadband beamforming with sidelobe control” by Shefeng Yan et al. (J. Acoust. Soc. Am. 121 (1), January 2007) describes an approach based on FIR filters and a method for optimizing the FIR filters for e.g. minimum sidelobe level of the beamformer.
The optimized broadband Filter-And-Sum (FAS) beamforming is able to significantly reduce the side-lobe level relative to Delay-And-Sum (DAS) beamforming and—for the case of spherical arrays—Spherical Harmonics Beamforming (SHB), see for example Shefeng Yan et al. (ibid.) and the article “Optimal Modal Beamforming for Spherical Microphone Arrays” by Shefeng Yan et al. (IEEE Transactions on Audio, Speech and Language Processing, Vol. 19, No. 2, February 2011, 361-371).
However, the computation of the optimal filter parameters is a very heavy computational task as illustrated herein. In particular, in applications where beamforming operations are to be performed for many focus points and for large sensor arrays, the computational resources for performing prior art optimised broadband FAS beamforming may be prohibitive. Also, the method outlined by Shefeng Yan et al. (J. Acoust. Soc. Am, ibid) requires the optimization to be based on a covariance matrix of the signals from each particular measurement, introducing properties similar to those of Minimum Variance (or Capon) beamformers: The output is not a linear function of the sources in the sense that the output resulting from a measurement on two sources is not the sum of the outputs from measurements on each one of the two sources separately.